arcsin05

The arcsin05, often written as arcsin(0.5) or sin⁻¹(0.5), refers to the angle whose sine is 0.5. In the context of trigonometry, the arcsine function is the inverse of the sine function. It answers the question: "What angle, when its sine is taken, results in the value 0.5?"

The principal value of arcsin(0.5) is typically considered within the range of -π/2 to π/2 radians, or -90° to 90° degrees. Within this range, the angle whose sine is 0.5 is π/6 radians, which is equivalent to 30 degrees. This is a common value encountered in geometry and trigonometry, particularly in relation to equilateral triangles and 30-60-90 right triangles.

It's important to note that the sine function is periodic, meaning that there are infinitely many angles whose sine is 0.5. For example, 5π/6 radians (150°) also has a sine of 0.5. However, by convention, the arcsine function returns the principal value. When solving equations involving arcsine, all possible solutions may need to be considered depending on the specific problem. The value of arcsin(0.5) is a fundamental concept in understanding inverse trigonometric functions.